Easy GRE question: Statistics?

Question

I'm not sure how to set this statistics problem when they give me a group of arbitrary values. Can someone help? A group of 20 values has a mean of 85 and a median of 80. A different group of 30 values has a mean of 75 and a median of 72. a) What is the mean of the 50 values? b) What is the median of the 50 values?

Answer 1

For the combined means, it is important to remember what a mean represents. It is the sum of the values for the sample divided by the sample size. So if the mean of the first group is 85 and the sample size is 20, you know that the sum of the values for the first group is 1700 (20*85). For group 2, the sum would be 2250 (30*75). So if you wanted to find the combined mean, you would add the two sums (1700 + 2250) and then divide by the total sample size (20 + 30). The result here would be 79 (3950/50).

As for combining two medians with just summary statistics, that is not possible. You would need to have access to the 50 data points and then calculate the median of the combined sample. With just the information provided here, there would be insufficient information to solve B.

Hope this was helpful!

Answer 2

Mean: (20(85) + 30(75))/50 = 79. Notice how the overall mean is a weighted average of the 2 individual means.

Median: There is no way to determine the exact median without additional information. All that is certain is that the resulting median must be between the 2 individual medians, so between 72 and 80.